A method for reducing or eliminating bias instability in a SBS laser gyroscope comprises introducing a first pump signal propagating in a CW direction, and a second pump signal propagating in a CCW direction in a resonator; generating a CCW first-order SBS signal and a CW first-order SBS signal in the resonator; increasing a power level of the first pump signal above a threshold level such that the CW first-order SBS signal generates a CCW second-order SBS signal; and increasing a power level of the second pump signal above the threshold level such that the CCW first-order SBS signal generates a CW second-order SBS signal. Above the threshold level, an intensity fluctuation of the first-order SBS signals disappear and their DC power are clamped at substantially the same power level. A Kerr effect bias instability of the SBS laser gyroscope is reduced or eliminated by the clamped first-order SBS signals.